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Of butterflies, snowboarders, tornados and avalanches

Monday, April 7th, 2014

[ by Charles Cameron -- deeply uncertain as to how often he should be grateful for narrow escapes from troubles he was utterly unaware of ]
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See, the first thing I want to know it: is an oblivious butterfly’s wing-flap roughly equivalent to an oblivious snowboader’s short slide across snow? And the second: is a tornado roughly comparable to an avalanche? I mean, a second’s worth of a living creature’s movement in the one case, and a “natural disaster” of somewhat larger proportions in the other?

Of course, the avalanche was closer to the snowboarder, who wound up “riding” it to safety, than Brazil is to Texas. Is that a difference that makes a difference?

The first quote above is from Laura Zuckerman‘s Reuters report, No charges for snowboarder who triggered killer Montana avalanche, posted yesterday, and the second is the title of a celebrated talk given to the American Association for the Advancement of Science by Edward Lorenz on December 29, 1972.

Although if it had been given just 3 days later (a very mild change in initial conditions) it would have been given not merely on a different day and to a different audience, but in a different month and a different year… and maybe even mentioned first in different editions of Encyclopedia Britannica and the OED!

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Well, see, I am also interested because in the paper with that intriguing title, Lorenz also said:

You can fill the lower panel with your own conclusion as to the question of the snowboarder: is there one of them helping us avoid an avalanche for very one that sets one going? Does it all cancel out in the long run?

From Zuckerman’s article again, broadening our scope from one incident in Montana to see the wider picture:

Almost all U.S. avalanches that affect people strike in the backcountry of the mountainous West and are caused by snowmobilers, skiers and snowboarders who inadvertently trigger them. Avalanches have killed 26 people so far this season, records show.

How many avalanches have we already missed this year thanks to other snowmobilers, skiers and snowboarders? And have we expressed our gratitude?

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On a somewhat similar tack, I wrote back in 2009:

A deer crossed perhaps twelve feet ahead of my car on the road from Sedona, Arizona to Cottonwood a year or two back. 60 mph is 88 feet per second. A tenth of a second later and the deer and or I would likely have been dead — one full second later, he or she would have crossed sixty feet behind me and I would have seen nothing, known nothing.

There are deer constantly crossing our paths sixty feet behind us — and it’s a normal day at the office, it’s one more day like any other: sunny, then partly cloudy, with a ten percent chance of rain.

Another time, and this was in Southern California, my car skidded out of control on a slick road as I was driving home with son Emlyn (then age 10). We hit the 3′ concrete center divider, jumped it, and flipped over, landing upside down. Emlyn and I climbed out with minor scratches — making sure we could climb out through the squished windows was the main issue. We were unscathed, but the car itself was totalled.

Had I taken that turn three seconds earlier or later, hitting a slicker or drier patch of road, and angling more or less steeply at the center divider — would we have been, in words made famous by wanted posters long before Schrodinger’s cat pondered them: Dead or Alive

Who knows?

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I suspect we have no idea how many close shaves and narrow escapes we have over the course of a lifetime — but the Recording Angel might know, and be in a state of perpetual hysterics over our ability to ignore a dozen near-disasters while getting totally discombobulated over a very minor incident that we happen to notice…

Unless the Recording Angel, too, is subject to Heisenberg‘s uncertainty and Schrodinger’s collapse…

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Of visionary rings, chariots — and tanks

Monday, March 17th, 2014

[ by Charles Cameron -- responding to Steve Engel's comment on my post Purim, or Israel vs Iran redux? ]
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Steve picked up on the image of the Merkabah, Ezekiel‘s visionary chariot as five wheels with wings in his comment today:

noting their resemblance to the Olympic rings. Such patterns have fascinated artists and symbolic thinkers across the centuries.

Thus the Abbot Joachim of Fiore portrayed the three “ages” of Father, Son and Holy Spirit as interlinked rings in his celebrated Liber Figurarum:

Cosimo de Medici, in the Renaissance, used the symbol of three interlocking “Borromean” rings on a medallion:

and indeed, Botticelli paints Pallas wearing the Medici triple rings in his painting, Pallas and the Centaur:

Jan Valentin Saether favors the Vesica Piscis formed where two circles overlap as the visionary aperture in the ninth image of his Viloshin Letters:

And the Olympic rings, as befits a logo heavily associated with advertising, might be the most banal of them all — had it not been redeemed one night by the gracious moon hanging low under London Bridge:

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But let us return to Ezekiel’s angelic wheels, which are related to early Jewish “mysticism of the Chariot” or Merkabah:

The Merkabah…

Can we find some echo of those wheels, perhaps, in the roadwheels of the IDF Armored Corps’s Merkava IV tank? Pictured here is the Mark I, from 1979.

Production of the Mark IV continues…

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Warren McCulloch’s lifetime koan

Saturday, March 15th, 2014

[ by Charles Cameron -- from intuitive leap to confirmation in a celebrated paper by neurophysiologist and cybernetician Warren McCulloch ]
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As I mentioned in my earlier post, Close reading, Synoptic- and Sembl-style, for parallels, patterns, there are times when my HipBone-influenced style of reading suggests the presence of a hidden piece of text that forms the basis for the part that’s readily available — in that case, the Qur’anic passage on which a major speech by Bin Laden was based.

Something very similar happened the other day, while I was reading the cybernetician Warren McCulloch‘s paper What is a number, that a man may know it, and a man, that he may know a number? thoroughly for the first time.

McCulloch’s title itself triggered an intuitive leap — call it a HipBone / Sembl move — to the Prologue to St John’s Gospel, familiar to me since my altar-boy childhood as the Last Gospel recited by the priest at the end of Mass.

I’ll have more to say about St John’s Prologue, and scripture more generally, later in this post, when I’ve told you how my “intuitive leap” was confirmed by further readings, and what that means in terms of intuition and verification.

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I call that move from McCulloch to St John an intuitive leap — but as with all such leaps, it is important to verify that the leap is well-founded at both ends.

Reading on past the title, then, I found McCulloch’s description of his own background, which is relevcant here:

I was destined for the ministry. Among my teen-age acquaintances were Henry Sloan Coffin, Harry Emerson Fosdick, H. K. W. Kumm, Hecker – of the Church of All Nations – sundry Episcopalian theologians, and that great Quaker philosopher, Rufus Jones.

In the fall of 1917, I entered Haverford College with two strings to my bow – facility in Latin and a sure foundation in mathematics. I “honored” in the latter and was seduced by it. That winter Rufus Jones called me in. “Warren,” said he, “what is thee going to be?” And I said, “I don’t know.” “And what is thee going to do?” And again I said, “I have no idea; but there is one question I would like to answer: What is a number, that a man may know it, and a man, that he may know a number?” He smiled and said, “Friend, thee will be busy as long as thee lives.”

In Zen (Buddhist) parlance, Rufus Jones is telling Warren McCulloch that he has found an authentic koan, a paradox to explore and deepen into, sufficient for a lifetime.

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It’s only a little later in McCulloch’s paper that my intuitive leap is “verified” in McCulloch’s own words:

This lecture might be called, “In Quest of the Logos” or, more appropriately – perverting St. Bonaventura’s famous title – “An Itinerary to Man.” Its proper preface is that St. Augustine says that it was a pagan philosopher – a Neoplatonist – who wrote, “In the beginning was the Logos, without the Logos was not anything made that was made … So begins our Christian theology.”

But McCulloch doesn’t stop there, he continues right on from theology into mathematics:

So begins our Christian theology. It rests on four principles. The first is the eternal verities. Listen to the thunder of that saint, in about A.D. 500: “7 and 3 are 10; 7 and 3 have always been 10; 7 and 3 at no time and in no way have ever been anything but 10; 7 and 3 will always be 10. I said that these indestructible truths of arithmetic are common to all who reason.” An eternal verity, any cornerstone of theology is a statement that is true regardless of the time and place of its utterance. Each he calls an idea in the Mind of God, which we can understand but can never comprehend.

The idea (“mathematics”) and the thinker (“man”) — McCulloch is working at the interface of “mind and matter” — “word and flesh” — the eternal and the temporal. He’s working at what is these days called the “hard problem of consciousness”.

St John, too, was working at that interface, and brilliantly so — regardless of what credence you put in his theology of the Incarnation of God in Man, it is a brilliant attempt to join the Hebrew “In the Beginning” of Genesis with the Greek “In the Beginning” of his own writings.

My own point here is this: that an intuitive leap, once made, needs to be grounded or confirmed by slower, more explicit, rational or experimental means.

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Having made my point, I’d like to add some further notes here, for those interested in scriptural matters…

Here’s John 1.1-14, the celebrated “Prologue” to St John’s Gospel, in the King James version, worth reading whether you know it or not for the comparison that follows with St Augustine’s stunnning reading of the same text:

In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not.

There was a man sent from God, whose name was John. The same came for a witness, to bear witness of the Light, that all men through him might believe. He was not that Light, but was sent to bear witness of that Light.

That was the true Light, which lighteth every man that cometh into the world. He was in the world, and the world was made by him, and the world knew him not. He came unto his own, and his own received him not. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.

And the Word was made flesh, and dwelt among us, and we beheld his glory, the glory as of the only begotten of the Father, full of grace and truth.

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Here is Augustine’s comment, from his Confesssions, book VII:

Thou procuredst for me, by means of one puffed up with most unnatural pride, certain books of the Platonists, translated from Greek into Latin. And therein I read, not indeed in the very words, but to the very same purpose, enforced by many and divers reasons, that In the beginning was the Word, and the Word was with God, and the Word was God: the Same was in the beginning with God: all things were made by Him, and without Him was nothing made: that which was made by Him is life, and the life was the light of men, and the light shineth in the darkness, and the darkness comprehended it not. And that the soul of man, though it bears witness to the light, yet itself is not that light; but the Word of God, being God, is that true light that lighteth every man that cometh into the world. And that He was in the world, and the world was made by Him, and the world knew Him not. But, that He came unto His own, and His own received Him not; but as many as received Him, to them gave He power to become the sons of God, as many as believed in His name; this I read not there.

Again I read there, that God the Word was born not of flesh nor of blood, nor of the will of man, nor of the will of the flesh, but of God. But that the Word was made flesh, and dwelt among us, I read not there.

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That quote from St Augustine is a striking one — by way of comparison I would like to offer this no-less fascinating excerpt from the Islamic historiographer Ibn Khaldun‘s Muqaddimah, describing developments in the early church from the death of Christ to the establishment of the canon of scriptures:

The Apostles divided into different groups. Most of them went to the country of the Romans and made propaganda for the Christian religion. Peter was the greatest of them. He settled in Rome, the seat of the Roman emperors. They 420 then wrote down the Gospel that had been revealed to Jesus, in four recensions according to their different traditions. Matthew wrote his Gospel in Jerusalem in Hebrew. It was translated into Latin by John, the son of Zebedee, one of (the Apostles). (The Apostle) Luke wrote his Gospel in Latin for a Roman dignitary. (The Apostle) John, the son of Zebedee, wrote his Gospel in Rome. Peter wrote his Gospel in Latin and ascribed it to his pupil Mark. These four recensions of the Gospel differ from each other. Not all of it is pure revelation, but (the Gospels) have an admixture of the words of Jesus and of the Apostles. Most of (their contents) consists of sermons and stories. There are very few laws in them.

The Apostles came together at that time in Rome and laid down the rules of the Christian community. They entrusted them to Clement, a pupil of Peter, noting in them the list of books that are to be accepted and in accordance with which one must act…

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Theology, once the Queen of Sciences and now largely ignored, has been laying fallow for centuries. There are rich findings here for those who choose to dig.

h/t Derek Robinson.

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On the felicities of graph-based game-board design: preliminaries

Thursday, March 6th, 2014

[ by Charles Cameron -- on graph theory, and the background and history of HipBone / Sembl gameboards ]
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First off, a graph — at least the way I’m using it here — is a diagram of linkages. The items linked, which may be people, places, phones, ideas, quantities, whatever, are represented by dots or circles, known as nodes, and the links between them by lines, known as edges.

Here’s a simple graph diagram with four nodes and seven edges:

left: a simple graph, based on, right: the bridges of the city of Königsberg circa 1735

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That diagram represents — elegantly, with topological accuracy — the seven bridges connecting the banks and islands of the city of Königsberg — which gavs rise to a famous math problem, which in turn gave rise to that branch of mathematics we now know as Graph Theory.

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Graphs are thus pictures of networks, and networks are the non-linear, feedback-capable basis for an astonishing variety of interesting things such as the internet and your and my brains

And they can get pretty complex. I’m a simple soul, and not a great network maven — but here’s what my network in LinkedIn looks like as of today. It too is a graph, although it reminds me of broccoli, or of a fish…


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Hey, that’s a pretty small network — and graph — compared with, say, a graph of all the neurons in a single brain, all the brains on the world’s computer networks, or all the neurons in all the brains on all the networks…

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Graphs with concepts at the nodes and conceptual links along the edges have been used for centuries to convey mystical states, propositions in theology, and concepts in the natural sciences:

Left, the Sephirotic Tree in Kabbalah; middle, the four elements in Oronce Fine; right, the Christian Trinity

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So you won’t be too surprised to learn that my variants on the Glass Bead Game of Hermann Hesse, which are designed to build what he termed the “hundred-gated cathedral of Mind” by analogically connecting the great thoughts of human-kind across all the arts and scences, use graphs (in this sense) as their boards…

Here, for instance, is one possible board design, derived from the inner vaulting of an English cathedral roof:

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Okay, past is prelude.

In the second part of this post I’ll show you a series of boards actually used in HipBone / Sembl play, and then two dazzling works — one a work of art, the other a work of science — that leapt out at my in the course of my browsing a morning or two ago…

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A DoubleQuote in the (Arctic) Wild

Friday, January 3rd, 2014

[ by Charles Cameron -- always on the lookout for intriguing double-images ]
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There’s an implied “this is to that as this is to that” double analogy here. Just how well or ill it teaches coordinate systems I leave to others to decide — even without the analogical joking though, it’s an intriguing visual juxtaposition.

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